# Computations
import numpy as np
import pandas as pd
import re

from sklearn import preprocessing

# Visualisation libraries

## Text
from colorama import Fore, Back, Style
from IPython.display import Image, display, Markdown, Latex, clear_output

## progressbar
import progressbar

## plotly
from plotly.offline import init_notebook_mode, iplot 
import plotly.graph_objs as go
import plotly.offline as py
from plotly.subplots import make_subplots
import plotly.express as px

## seaborn
import seaborn as sns

## matplotlib
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse, Polygon
from matplotlib.font_manager import FontProperties
import matplotlib.colors as mcolors
plt.style.use('seaborn-whitegrid')
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
plt.rcParams['text.color'] = 'k'
%matplotlib inline

import warnings
warnings.filterwarnings("ignore")

Home / Healthcare Analytics and Modeling

Pima Indians Diabetes Dataset

• Preprocessing
• Modeling: Gradient Boosting Classifier with Feature Ranking

Pima Indians Diabetes Dataset

In this article, we use Kaggle'sPima Indians Diabetes. The Pima Indians are a group of Native Americans living in an area consisting of what is now central and southern Arizona. A variety of statistical methods are used here for predictions.

Context

This dataset is originally from the National Institute of Diabetes and Digestive and Kidney Diseases. The objective of the dataset is to diagnostically predict whether or not a patient has diabetes, based on certain diagnostic measurements included in the dataset. Several constraints were placed on the selection of these instances from a larger database. In particular, all patients here are females at least 21 years old of Pima Indian heritage.

Content

The datasets consist of several medical predictor variables and one target variable, Outcome. Predictor variables include the number of pregnancies the patient has had, their BMI, insulin level, age, and so on.

Preprocessing

Path = 'pima-indians-diabetes-database/diabetes.csv'
Data = pd.read_csv(Path)
Data.columns = [re.sub(r"(\w)([A-Z])", r"\1 \2", x).replace('B MI','BMI') for x in Data.columns]
display(Data.head())
display(pd.DataFrame({'Number of Instances': [Data.shape[0]], 'Number of Attributes': [Data.shape[1]]}).style.hide_index())
Target = 'Outcome'
Labels = ['Non-Diabetic', 'Diabetic']

	Pregnancies	Glucose	Blood Pressure	Skin Thickness	Insulin	BMI	Diabetes Pedigree Function	Age	Outcome
0	6	148	72	35	0	33.6	0.627	50	1
1	1	85	66	29	0	26.6	0.351	31	0
2	8	183	64	0	0	23.3	0.672	32	1
3	1	89	66	23	94	28.1	0.167	21	0
4	0	137	40	35	168	43.1	2.288	33	1

Number of Instances	Number of Attributes
768	9

Feature	Explanations
Pregnancies	Number of times pregnant
Glucose	Plasma glucose concentration a 2 hours in an oral glucose tolerance test
BloodPressure	Diastolic blood pressure (mm Hg)
SkinThickness	Triceps skinfold thickness (mm)
Insulin	2-Hour serum insulin (mu U/ml)
BMI	Body mass index (weight in kg/(height in m)^2)
DiabetesPedigreeFunction	Diabetes pedigree function
Age	Age (years)
Outcome	Whether or not a patient has diabetes

def Data_Plot(Inp, W = False):
    data_info = Inp.copy()
    data_info = Inp.dtypes.astype(str).to_frame(name='Data Type')
    Temp = Inp.isnull().sum().to_frame(name = 'Number of NaN Values')
    data_info = data_info.join(Temp, how='outer')
    data_info ['Size'] = Inp.shape[0]
    data_info['Percentage'] = 100 - np.round(100*(data_info['Number of NaN Values']/Inp.shape[0]),2)
    data_info = data_info.reset_index(drop = False).rename(columns = {'index':'Features'})
    #
    fig = px.bar(data_info, x= 'Features', y= 'Percentage', color = 'Data Type', text = 'Data Type',
                color_discrete_sequence = ['PaleGreen', 'LightCyan', 'PeachPuff', 'Pink', 'Plum'],
                 hover_data = data_info.columns)
    fig.update_layout(plot_bgcolor= 'white', legend=dict(x=1.01, y=.5, traceorder="normal",
                                                         bordercolor="DarkGray", borderwidth=1))
    fig.update_traces(texttemplate= 6*' ' + '%{label}', textposition='inside')
    fig.update_traces(marker_line_color= 'Black', marker_line_width=1., opacity=1)
    if W:
        fig.update_layout(width = W)
    fig.update_layout(title={'text': '<b>' + 'Dataset Overview' + '<b>', 'x':0.5,
                             'y': 0.92, 'xanchor': 'center', 'yanchor': 'top'}, yaxis_title='Frequency')
    fig.show()
    return data_info
    
    
_ = Data_Plot(Data, W = 800)

Let's take a close look at our data.

fig, ax = plt.subplots(nrows=4, ncols=2, figsize = (16, 20))
ax = ax.ravel()
for i in range(len(Data.columns[:-1])):
    sns.distplot(Data.iloc[:,i], rug=True, rug_kws={"color": "red"},
                 kde_kws={"color": "k", "lw": 2, "label": "KDE"}, hist_kws={"histtype": "step", "linewidth": 2,
                                                                            "alpha": 1, "color": "Navy"}, ax= ax[i])

Temp = ['Non-Diabetic' if x==0 else 'Diabetic' for x in Data['Outcome']]
fig = go.Figure(data=go.Splom(dimensions=[dict(label='Pregnancies', values=Data['Pregnancies']),
                              dict(label='Glucose', values=Data['Glucose']),
                              dict(label='Blood<br>Pressure', values=Data['Blood Pressure']),
                              dict(label='Skin<br>Thickness', values=Data['Skin Thickness']),
                              dict(label='Insulin', values=Data['Insulin']),
                              dict(label='BMI', values=Data['BMI']),
                              dict(label='Diabetes<br>Pedigree<br>Fun', values=Data['Diabetes Pedigree Function']),
                              dict(label='Age', values=Data['Age'])],
                              showupperhalf=False,
                              marker=dict(color=Data['Outcome'], size=4, colorscale='Bluered',
                              line=dict(width=0.4, color='black')),
                              text=Temp, diagonal=dict(visible=False)))
del Temp
fig.update_layout(title='Scatterplot Matrix', dragmode='select',
                  width=900, height=900, hovermode='closest')
fig.show()

Normalizing the Data

As can be seen, the Data has a normal distribution, and some entries need to be adjusted. In doing so, we defined a normalizer as follows, for a given vector $x$,

\begin{align*} \text{Normalizer}(x, cut) = \begin{cases} x_i &\mbox{if } |x_i- \mu|<\sigma\times cut \\ mode(x) & \mbox{else} \end{cases}. \end{align*}

def Normalizer(Col, cut = 3):
    return Col[(Col > (Col.mean() - Col.std() * cut)) &
               (Col < (Col.mean() + Col.std() * cut))]

# Normalized Data
df = Data.copy()

fig, ax = plt.subplots(nrows=4, ncols=2, figsize = (16, 20))
ax = ax.ravel()

for i in range(len(df.columns[:-1])):
    df[df.columns[i]] = Normalizer(Data[Data.columns[i]])
    df[df.columns[i]] = df[df.columns[i]].fillna(df[df.columns[i]].dropna().mode()[0])
    # Sub-Plots
    sns.distplot(df.iloc[:,i], rug=True, rug_kws={"color": "red"}, kde_kws={"color": "k", "lw": 2, "label": "KDE"},
                 hist_kws={"histtype": "step", "linewidth": 2, "alpha": 1, "color": "Navy"}, ax= ax[i])

Basically, we diminished the influence of certain data points (see the following figure).

Temp = Data.copy()
Temp.iloc[:,:-1] = abs(Data.iloc[:,:-1] - df.iloc[:,:-1])

Temp0 = ['Non-Diabetic' if x==0 else 'Diabetic' for x in Temp['Outcome']]

fig = go.Figure(data=go.Splom(dimensions=[dict(label='Pregnancies', values=Temp['Pregnancies']),
                              dict(label='Glucose', values=Temp['Glucose']),
                              dict(label='Blood<br>Pressure', values=Temp['Blood Pressure']),
                              dict(label='Skin<br>Thickness', values=Temp['Skin Thickness']),
                              dict(label='Insulin', values=Temp['Insulin']),
                              dict(label='BMI', values=Temp['BMI']),
                              dict(label='Diabetes<br>Pedigree<br>Fun', values=Temp['Diabetes Pedigree Function']),
                              dict(label='Age', values=Temp['Age'])],
                              showupperhalf=False,
                              marker=dict(color=Temp['Outcome'], size=4, colorscale='Bluered',
                              line=dict(width=0.4, color='black')),
                              text=Temp0, diagonal=dict(visible=False)))
del Temp, Temp0
fig.update_layout(title='Scatterplot Matrix', dragmode='select',
                  width=900, height=900, hovermode='closest')
fig.show()

Data Correlation

def Correlation_Plot (Inp, Fig_Size = 12, annot_kws = 11):
    Correlation_Matrix = Inp.corr().round(2)
    mask = np.zeros_like(Correlation_Matrix)
    mask[np.triu_indices_from(mask)] = True
    for i in range(len(mask)):
        mask[i,i]=0
    fig, ax = plt.subplots(figsize=(Fig_Size, Fig_Size))
    sns.heatmap(Correlation_Matrix, ax=ax, mask=mask, annot=True, square=True, 
                cmap =sns.color_palette("Greens", n_colors=10), linewidths = 0.2, vmin=0, vmax=1,
                cbar_kws={'label': 'Correlation', "aspect":30, "shrink": .4},  annot_kws={"size": annot_kws})
    return Correlation_Matrix

_ = Correlation_Plot (df, 9)

	Pregnancies	Glucose	Blood Pressure	Skin Thickness	Insulin	BMI	Diabetes Pedigree Function	Age	Outcome
Pregnancies	1.00	0.12	0.22	-0.10	-0.07	0.02	0.02	0.55	0.20
Glucose	0.12	1.00	0.22	0.05	0.22	0.23	0.10	0.27	0.49
Blood Pressure	0.22	0.22	1.00	0.02	-0.06	0.26	0.03	0.33	0.16
Skin Thickness	-0.10	0.05	0.02	1.00	0.45	0.37	0.15	-0.12	0.06
Insulin	-0.07	0.22	-0.06	0.45	1.00	0.14	0.18	-0.07	0.08
BMI	0.02	0.23	0.26	0.37	0.14	1.00	0.12	0.06	0.31
Diabetes Pedigree Function	0.02	0.10	0.03	0.15	0.18	0.12	1.00	0.07	0.19
Age	0.55	0.27	0.33	-0.12	-0.07	0.06	0.07	1.00	0.26
Outcome	0.20	0.49	0.16	0.06	0.08	0.31	0.19	0.26	1.00

Export to a CSV file

df.to_csv (Path.split(".")[0]+'_mod.csv', index = None, header=True)

X and y sets

X = Data.drop(columns = [Target])
y = Data[Target]

Features with high variance

Moreover, high variance for some features can hurt our modeling process. For this reason, we would like to standardize features by removing the mean and scaling to unit variance.

X = pd.DataFrame(data = X, columns = X.columns)
# scaling data
scaler = preprocessing.StandardScaler()
X_std = scaler.fit_transform(X)
X_std = pd.DataFrame(data = X_std, columns = X.columns)
del scaler

fig, ax = plt.subplots(2, 1, figsize=(12, 8))
ax = ax.ravel()
font = FontProperties()
font.set_weight('bold')
CP = [sns.color_palette("OrRd", 20), sns.color_palette("Greens", X.shape[1])]
Names = ['Variance of the Features', 'Variance of the Features (Standardized)']
Sets = [X, X_std]
kws = dict(label='Feature\nVariance', aspect=10, shrink= .3)
for i in range(len(ax)):
    Temp = Sets[i].var().sort_values(ascending = False).to_frame(name= 'Variance').round(2).T
    _ = sns.heatmap(Temp, ax=ax[i], annot=True, square=True,  cmap = CP[i],
                    linewidths = 0.8, vmin=0, vmax=Temp.max(axis =1)[0],  annot_kws={"size": 14},
                    cbar_kws=kws)
    _ = ax[i].set_yticklabels('')
    _ = ax[i].set_title(Names[i], fontproperties=font, fontsize = 14)
    del Temp

df[X.columns] = X_std.copy()
df.to_csv (Path.split(".")[0]+'_STD.csv', index = None, header=True)
del CP, Names, ax, fig, font, Sets, kws, X_std

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References

1. Smith, J. W., Everhart, J. E., Dickson, W. C., Knowler, W. C., & Johannes, R. S. (1988). Using the ADAP Learning Algorithm to Forecast the Onset of Diabetes Mellitus. Proceedings of the Annual Symposium on Computer Application in Medical Care, 261–265.

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